## Concentration of solutions

When a solid dissolves in a liquid a mixture is formed. The solid that dissolves in a liquid is called the solute, the liquid is called the solvent and the mixture formed is called the solution. The “strength” of the solution formed is called its concentration. For example, a cup of water that contains 5 spoons of sugar has a higher concentration of sugar than one that contains 2 spoons of sugar. In this case, sugar is the solute and the water is the solvent.

The concentration of a solution is the amount of solute dissolved in a solvent.

The amount of solute in the solution can be expressed in terms of moles or as a mass in grams. The volume of solution is usually expressed in dm3, whereby 1 dm3 = 1 000 cm3.

### Concentration of a solution using number of moles

The molar concentration of a solution is the number of moles of solute in 1 dm3 of a solvent.

#### Formula for calculating concentration in terms of moles

$latex Concentration = \frac{Number\ of\ moles\ of\ solute}{volume\ of\ Solvent}$

The units are mol/dm3.

#### Question

27 g of aluminium burns in chlorine to form 133.5 g of aluminium chloride.

1. What mass of chlorine is present in 133.5 g of aluminium chloride?
2. How many moles of chlorine atoms is in 133.5 g of aluminium chloride?
3. How many moles of aluminium atoms are present in 27 g of aluminium?
4. Use your answers from above to find the simplest formula of aluminium chloride.
5. 2 000 cm3 of an aqueous solution is made using 13.35 g of aluminium chloride. What is its concentration in moles per dm3?

1. We are given that 27 g of aluminium burns in chlorine to form 133.5 g of aluminium chloride.Therefore, mass of chlorine = mass of aluminium chloride – mass of aluminium

= 133.5 g – 27 g

= 106.5 g

2. We know that:
• the mass of chlorine in 133.5 g of aluminium chloride = 106.5 g.
• molar mass of chlorine atoms = 35.5 g/mol

$latex Number\ of\ moles\ = \frac{mass}{molar\ mass}$

$latex = \frac{106.5\ g}{35.5\ g/mol}$

= 3 moles of chlorine atoms.

3. $latex Number\ of\ moles\ = \frac{mass}{molar\ mass}$$latex = \frac{27\ g}{27\ g/mol}$

= 1 moles of aluminium atoms.

4. Since the ration of aluminium:chlorine in aluminium chloride = 1:3 the simplest formula of aluminium chloride is AlCl3.
5. The concentration is needed in mol/dm3 so we convert the given mass to moles and the given volume to dm3.$latex Volume = \frac{2\ 000\ dm^3}{1\ 000}$

= 2 dm3

$latex Number\ of\ moles = \frac{mass}{molar\ mass}$

$latex = \frac{13.35}{27 + (35.5 \times 3)}$

= 0.1 moles of aluminium chloride.

$latex Concentration = \frac{number\ of\ moles}{volume}$

$latex = \frac{0.1}{2}$

= 0.05 mol/dm3

### Concentration of a solution using grams

The mass concentration of a solution is the mass of solute in 1 dm3 of a solvent.

#### Formula for calculating concentration in terms of moles

$latex Concentration = \frac{Mass\ of\ solute}{volume\ of\ Solvent}$

The units are g/dm3.

#### Example – A solution contains 23 grams of sodium chloride in 1 dm3 of water. Find its concentration in g/dm3.

$latex Concentration = \frac{Mass\ of\ solute}{volume\ of\ Solvent}$

$latex = \frac{23}{1}$

= 23 g/dm3.

### Molarity of a solution

The molarity of a solution (M) is its molar concentration.

This means that:

• a 1 M solution has a concentration of 1 mol/dm3.
• a 5 M solution has a concentration of 5 mol/dm3.

### Calculating amount of solute dissolved in a solution, given its concentration

Given the concentration and volume of a solution we can find the number of moles of solute as follows:

Number of moles = Concentration × Volume

N = CV

#### Example – How many moles of solute are in a 500 cm3 of solution, of concentration 2 mol/dm3?

V = 500 cm3 = 0.5 dm3

N = CV

= 2 × 0.5

= 1 mole.

#### Example – How many moles of solute are in 2 litres of solution, of concentration 0.5 mol/dm3?

V = 2 litres = 2 dm3

N = CV

= 2 × 0.5

= 1 mole.